Question

Consider the line that passes through each pair of given points, and decide what type of slope the line has.

(2, 4) and (5, 1)
undefined slope
(3,5) and (-1,2)
negative slope
(-7, 8) and (-7,0)
positive slope
(6.-3) and (4, -3)
zero slope

Answer 1

The slope of line through (2, 4) and (5, 1) is Negative

The slope of line through (3,5) and (-1,2) is Positive

The slope of line through (-7, 8) and (-7,0) is Undefined

The slope of line through (6.-3) and (4, -3) is Zero

Explanation:

Slope is defined as the steepness of a line.

Slope is denoted by m and the formula for calculating slope is:

`m = (y_2-y_1)/(x_2-x_1)`

Here

(x1,y1) and (x2,y2) are coordinates of the points through which the line passes

Now,

For (2, 4) and (5, 1):

`m = (1-4)/(5-2) = (-3)/(3) =-1`

NEGATIVE

For (3,5) and (-1,2)

`m = (2-5)/(-1-3) = (-3)/(-4) = (3)/(4)`

POSITIVE

For (-7, 8) and (-7,0)

`m = (0-8)/(-7+7) = (-8)/(0)`

UNDEFINED

For (6.-3) and (4, -3)

`m=(-3+3)/(4-6) = (0)/(-2) = 0`

ZERO

Hence,

The slope of line through (2, 4) and (5, 1) is Negative

The slope of line through (3,5) and (-1,2) is Positive

The slope of line through (-7, 8) and (-7,0) is Undefined

The slope of line through (6.-3) and (4, -3) is Zero